“Quietness” is valued as a characteristic of various types of products, such as automobiles, office equipment, household electric appliances, and houses. In order to increase the quietness of such products, materials having actions, such as sound absorption and sound insulation, are often used. Such materials are referred to as “acoustic materials”. An acoustic material may be constituted of a single material or of layered material, which includes layers of a plurality of materials laminated together.
The term “sound absorption” refers to the phenomenon in which sound incident to a material and is not reflected thereby and is absorbed or transmitted through the material. The performance of sound absorption is evaluated by a value such as sound absorption coefficient. The term “sound insulation” refers to the phenomenon in which sound incident to a material does not transmit through the material. The performance of sound insulation is evaluated by a value such as sound transmission loss. The sound absorption coefficient and the sound transmission loss are a function of the frequency, respectively. The sound absorption coefficient and the sound transmission loss are collectively referred to as “acoustic performance”.
In developing acoustic materials, it is a general practice to actually prototype an acoustic material, actually measure the acoustic performance of the prototype material, verify whether desired results have been obtained as a result of the measurement, and repeat the prototyping and the actual measurement until desired results are obtained. However, costs for the material may increase due to the repeated prototyping. In addition, dedicated facilities may be required to actually measure the acoustic performance of the prototype material. Furthermore, the development time often becomes long due to the prototyping and the actual measurement that must be repeated.
Instead of the method in which prototyping and actual measurement are repeated, a method is used in which an acoustic material is mathematically represented as a mathematical model and the acoustic performance of the acoustic material is calculated according to the mathematical model. In this method, characteristics of a material that is to be modeled, such as the density and the thickness of the material, i.e., values of material parameters, are determined. The acoustic performance of the material is calculated based on the values. Several mathematical models are available and the mathematical model to be used differs according to the type of the material to be modeled. Furthermore, the type of the material parameter that becomes necessary differs according to the mathematical model. Of course, if the acoustic material is a layered material, different mathematical model can be used for different materials.
For example, in the case of modeling porous materials, such as glass wool, the equivalent fluid model, rigid frame model, Biot model, and the like are used. For impervious elastic materials, such as a steel plate, a model different from those described above is used. In particular, the Biot model is described in Non Patent Literatures 1 to 3.
Among the several mathematical models described above, the Biot model will be specifically described. FIG. 1 illustrates the propagation of sound inside an acoustic material P, which is assumed in the Biot model. The acoustic material P is a porous material and includes frames F, which are a solid having elasticity, and air A, which exists among the frames F. Sound S1, which has been incident to the above-described acoustic material P, propagates through the air A as air-borne sound S2 and through the frames F as structure borne sound S3. The energy of the air-borne sound S2 is lost due to viscous loss L1 and heat exchange loss L2 in relation to the frame F. In addition, the energy of the structure borne sound S3 is lost due to internal loss L3. Further, an interaction M occurs between the air-borne sound S2 and the structure borne sound S3, by which the structure borne sound S3 is activated by the air-borne sound S2.
On the basis of FIG. 1, the Biot model uses nine material parameters, which include: (1) porosity; (2) flow resistivity; (3) tortuosity; (4) a viscous characteristic length; (5) a thermal characteristic length; (6) density; (7) an internal loss coefficient; (8) a shear modulus; and (9) a Poisson's ratio.
Among the above-described material parameters, (1) the porosity, (2) the flow resistivity, (3) the tortuosity, (4) the viscous characteristic length, and (5) the thermal characteristic length are parameters related to a fluid property of the acoustic material P, i.e., the air-borne sound S2. More specifically, the porosity refers to a ratio of air in the acoustic material P. As the ratio of the air A becomes greater, the porosity of the acoustic material P becomes higher. Next, the flow resistivity is a numerical value that represents the difficulty of air flow in the acoustic material P. Because sound is the vibration of air, if the flow resistivity of the acoustic material P is high, it becomes difficult for the air to flow inside the acoustic material P. In this case, the acoustic material P can be considered to be a material in which sound does not propagate readily. The flow resistivity is very important among the material parameters. The tortuosity is a numerical value that represents the complexity of the shape of paths of air, which are formed by the air A. As the tortuosity becomes higher, the sound propagates through the material P for a longer path, which brings about better sound absorption. The viscous characteristic length and the thermal characteristic length are a numerical value that represents the level of the viscous loss L1 and the level of the heat exchange loss L2, respectively.
Furthermore, among the above-described material parameters, (6) the density, (7) the internal loss coefficient, (8) the shear modulus, and (9) the Poisson's ratio are parameters related to an elastic property of the acoustic material P, i.e., the structure borne sound S3.
By solving a wave equation that uses the above-described nine material parameters, the wavenumber and the characteristic impedance of acoustic waves transmitted through the acoustic material P are obtained. To specifically describe the wavenumber, in the Biot model, three waves, i.e., a fast longitudinal wave, a slow longitudinal wave, and a shear wave propagate through the acoustic material P. In other words, the wavenumber of each of the three waves is obtained. Next, with respect to the characteristic impedance, for each of the fast longitudinal wave and the slow longitudinal wave, the characteristic impedance in the air existing in the air A and the characteristic impedance in the frame F are obtained. For the shear wave, the characteristic impedance in the frame F is obtained because it propagates through the frame F only. More specifically, five characteristic impedances are obtained in total for the above-described three waves. According to the Biot model, the acoustic performance of the acoustic material P can be calculated by using the above-described three wavenumbers and the five characteristic impedances.